In this talk, a framework for solving geometric reconstruction problems in computer vision will be presented based on the L-infinity norm. Instead of using the common sum-of-squares cost-function, that is, the L-2 norm, the model-fitting errors are measured using the L-infinity norm. Unlike traditional methods based on L-2, this framework allows for efficient computation of global estimates. It will be shown that a class of geometric structure and motion problems, for example, triangulation, camera resectioning and homography estimation can be recast as a quasi-convex optimization problem within the framework. These problems can be efficiently solved using Second Order Cone Programming (SOCP) and Bisection which are standard techniques in convex optimization. The methods have been validated on real data in different settings with small and large dimensions and with excellent performance.